Numerical Computations Concerning Landau-Siegel Zeros
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912873385558016 |
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| author | Lu, Rick F. Zaman, Asif Zhao, Haonan |
| author_facet | Lu, Rick F. Zaman, Asif Zhao, Haonan |
| contents | We computationally verify that if $L(s,χ)$ is a quadratic Dirichlet $L$-function modulo $q \leq 10^{10}$ then $L(σ,χ) \neq 0$ for real $σ\ge 1-1/(5\log q)$. The number of verified moduli exceeds benchmarks due to Watkins (2004), Platt (2016), and Languasco (2023) by a factor between 66 and 25,000. Our new algorithm draws from zero-free region arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03626 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Numerical Computations Concerning Landau-Siegel Zeros Lu, Rick F. Zaman, Asif Zhao, Haonan Number Theory 11M20 (Primary), 11M06 (Secondary) We computationally verify that if $L(s,χ)$ is a quadratic Dirichlet $L$-function modulo $q \leq 10^{10}$ then $L(σ,χ) \neq 0$ for real $σ\ge 1-1/(5\log q)$. The number of verified moduli exceeds benchmarks due to Watkins (2004), Platt (2016), and Languasco (2023) by a factor between 66 and 25,000. Our new algorithm draws from zero-free region arguments. |
| title | Numerical Computations Concerning Landau-Siegel Zeros |
| topic | Number Theory 11M20 (Primary), 11M06 (Secondary) |
| url | https://arxiv.org/abs/2602.03626 |